Critical points and resonance of hyperplane arrangements

D. Cohen; G. Denham; M. Falk; A. Varchenko

doi:10.4153/CJM-2011-028-8

Critical points and resonance of hyperplane arrangements

D. Cohen
, G. Denham
, M. Falk
, A. Varchenko

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

If Φ_λ is a master function corresponding to a hyperplane arrangement A and a collection of weights λ, we investigate the relationship between the critical set of Φ_λ, the variety defined by the vanishing of the one-form ωλ = d log and Φ_λ, the resonance of λ. For arrangements satisfying certain conditions, we show that if λ is resonant in dimension p, then the critical set of Φ_λ has codimension at most p. These include all free arrangements and all rank 3 arrangements.

Original language	English (US)
Pages (from-to)	1038-1057
Number of pages	20
Journal	Canadian Journal of Mathematics
Volume	63
Issue number	5
DOIs	https://doi.org/10.4153/CJM-2011-028-8
State	Published - Oct 2011

Keywords

Critical set
Hyperplane arrangement
Master function
Resonant weights

ASJC Scopus subject areas

General Mathematics

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abstract = "If Φλ is a master function corresponding to a hyperplane arrangement A and a collection of weights λ, we investigate the relationship between the critical set of Φλ, the variety defined by the vanishing of the one-form ωλ = d log and Φλ, the resonance of λ. For arrangements satisfying certain conditions, we show that if λ is resonant in dimension p, then the critical set of Φλ has codimension at most p. These include all free arrangements and all rank 3 arrangements.",

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AU - Falk, M.

AU - Varchenko, A.

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AB - If Φλ is a master function corresponding to a hyperplane arrangement A and a collection of weights λ, we investigate the relationship between the critical set of Φλ, the variety defined by the vanishing of the one-form ωλ = d log and Φλ, the resonance of λ. For arrangements satisfying certain conditions, we show that if λ is resonant in dimension p, then the critical set of Φλ has codimension at most p. These include all free arrangements and all rank 3 arrangements.

KW - Critical set

KW - Hyperplane arrangement

KW - Master function

KW - Resonant weights

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JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 5

ER -

Critical points and resonance of hyperplane arrangements

Abstract

Keywords

ASJC Scopus subject areas

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